To me it seems like it is a sine and cosine graph.
You would need to develop an equation to be able to calculate the area accurately:
Where a and b are constant values.
To me it seems its maximum is 4.5 and minimum is -4.5. Thus constant a must be 4.5.
One full cycle seems to be 2.0π. If you are working in radians, constant b must be /2. If working in degrees, b = 360/2.
(For working in radians)
There once you have your 2 equations, you can integrate between 0 and 2 to find the area.